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Toluene reacts with H2 to form benzene (B), but a side reaction occurs in which a by-product diphenyl (D) is formed:

C7H8          +       H2              ------------------>  C6H6     +     CH4                       (a)
Toluene              hydrogen                          benzene        methane


2C7H8          +       H2              ------------------>  C12H10     +    2 CH4              (b)


The process is shown in the figure below. Hydrogen is added to the gas recycle stream to make the ratio of H2 to Ch4 1 to 1 before the gas enters the mixer. The ratio of H2 to toluene entering the reactor at G is 4H2 to 1 toluene. The conversion of toluene to benzene on one pass through the reactor is 80%, and the conversion of toluene to the by-product diphenyl is 8% per pass. Calculate the moles of RG and moles RL per hour.

Data:  Compound:    H2      CH4       C2H6      C7H8      C12H10
                                    2          16            78           92           154



CHE 200 -Chemical Engineering Fundamentals Assignment question

Basis: 100 mol toluene (T) in stream G

consider:
a) system: Reactor + Separator
 
input - output + generation - consumption = 0

for toluene: 100 - RL + 0 - 100(0.8 + 0.08) = 0
for H2: 100(4) - nwH2 + 0 - 100(0.8 + 0.08) = 0
for CH4: 100(4) - nwCH4 + 100(0.8 + 0.08) = 0

RL = 12 mole
nwH2 = 316 mole
nCH4 = 488 mole

---

Total = 804 mole

b) system: Mixer + Make up point

for toluene: F+RL=100
for H2= M+RG(316/804)=100(4)
for CH4= RG(488/804)=100(4)

RG=659 mol
F=88 mol
M= 141 mol

moles of RG per hour?

(3450 lb/ hr) *  (lbmole/ 92 lb) = 37.5 lbmol/ hr toluene in F

(100 lbmol in G/ 88 lbmol in F) * (37.5 lbmol F/ 1 hr)* (659 lbmol RG/100 lbmol G) = 280.8 lbmol RG/hr

moles of RL per hour?

(100 lbmol in G/ 88 lbmol in F) * (37.5 lbmol F/ 1 hr) * (12 lbmol RL/ 100 lbmol in G) = 5.11 lbmol RL/hr

Thank you for your help  :)